How can I explain why the following sentence is poorly written?

I came across the following sentence in some instructions and it almost seems like a double negative to me, yet there are not two negations in it that I see, so I am wondering how to explain what intuitively feels wrong about this sentence:

All of these are not applicable to both events or people.

To me, this is more clearly written as:

Some of these are only applicable to either events or people.

Solution 1:

All... are not is always clunky, and should be replaced with None... is*:

None of these is applicable to both events and people.

Also note that both X or Y is incorrect, and should be replaced with both X and Y.

You created the second example by: 1. replacing not... both with only... either, (which is equivalent) and 2. replacing all with some (which is not equivalent). If you want to keep that changed meaning, your example seems fine:

Some of these are only applicable to either events or people.

*As @Karl points out below, another popular though technically incorrect interpretation of All... are not is Not all... are. If this is the intended meaning, then it would also be a better way to say it:

Not all of these are applicable to both events and people.

Solution 2:

Resorting to a tired rule like double-negation is a bad way to explain the problem in the first place. The problem with the sentence isn't that it breaks a rule of grammar, it's that it is confusing. I'm not even sure if your sentence means the same thing as the original one, because I don't know what the original one means.